International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 337-342

Permutation binomials

Charles Small1,2

1Department of Mathematics and Statistics, Queen's University, Ontario, Kingston K7L 3N6, Canada
2Department of Mathematics and Statistics, McMaster University, Ontario, Hamilton L8S 4K1, Canada

Received 7 June 1988; Revised 13 December 1988

Copyright © 1990 Charles Small. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A polynomial f over a finite feld F is a permutation polynomial if the mapping FF defined by f is one-to-one. We are concerned here with binomials, that is, polynomials of the shape f=aXi+bXj+c, i>j1. Even in this restricted setting, it is impossible to give general necessary and sufficient conditions on a, b, c for f to be a permutation polynomial. We review, and systematize, what is known.